In the context of signal processing, when a signal is transmitted to a receiving device, there is a certain amount of unknown delay associated with the propagation of the signal. The original signal is not received instantaneously at the receiving device. A calculated estimate of the delay associated with the received signal is generally limited to the resolution of the sampling rate of the received signal. For example, if the received signal can be represented as a continuous integrable function, x(t), then the received signal, which typically contains noise, may be converted to a discrete sequence of values in time through sampling. The discrete sequence of values is herein referred to as sampled data. As the sampling rate increases, the sampled data becomes a more accurate representation of x(t). Due to the finite sampling rate, the delay value that is calculated from the sampled data is not as precise as the delay value calculated from a continuous function.
In one approach, a more accurate delay value estimate may be obtained by adjusting the sampling times. For example, correlation calculations can be performed for a pair of delay values that produce equal values in the magnitude calculations of the correlation integrals. If the magnitude values corresponding to the pair of delay values are high enough, then it may be assumed that the peak magnitude, and hence the true time delay, lies halfway between the pair of delay values (used in the delay lock loop). However, a significant drawback with this approach is that it assumes that the sampling times can be adjusted, and that it is already known where to look approximately. If the sampling times cannot be adjusted, (i.e., the set of sampled data with which to work is fixed), then in general a different reference signal needs to be used in computing the correlation integrals at the different delay. It may not be enough to just time shift the reference by an integer number of samples. Another approach for estimating a delay value at a level of precision that is higher than the precision corresponding to the sampling rate, is to adopt a fine-grid for a hypothesized range of delay values. In such an approach, the sampled data is correlated against the reference signal by shifting the reference signal according to the fine gridding of delay values. The correlation between the received signal and the reference signal is performed by calculating the In Phase (“I”) and Quadrature (“Q”) correlation integrals for the range of hypothesized delay values, which is finely gridded, at the specified modulation frequency. But the finer the gridding of the search region gets, the more correlations must be computed. Thus, a disadvantage with using a fine grid for searching over the hypothesized range of delay values is that the high cost of computing the correlations, especially when there is a considerable amount of sampled data, (i.e., the sampling duration is long) can be computationally prohibitive. Based on the foregoing, there is a clear need for a technique for estimating the delay associated with a received signal in a cost effective fashion during signal processing.
A very similar problem arises when the received signal is modulated by an unknown frequency and one needs to derive a fine-tuned estimate of this frequency from a set of IQ correlations obtained by searching over a coarse-grained set of frequencies representing the uncertain region.